What is the solution for y^{''}-a^2*y+b=0 ?

The solution for y^{''}-a^2*y+b=0 is y=c_{1}e^{at}+c_{2}e^{-at}+b/(a^2)

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y^{''}-a^2*y+b=0

y^{^{''}} - a^{2} \cdot y + b = 0

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{b}{a ^{2}}

Solution steps

y^{''} (t) - a^{2} \cdot y + b = 0

Solve linear ODE:

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{b}{a ^{2}}

y = c_{1} e^{a t} + c_{2} e^{- a t} + \frac{b}{a ^{2}}

What is the solution for y^{''}-a^2*y+b=0 ?
The solution for y^{''}-a^2*y+b=0 is y=c_{1}e^{at}+c_{2}e^{-at}+b/(a^2)